A Reflection Calculus for Bar Induction and the Linearity of Consistency Strength Ordering

Fedor Pakhomov, Vlad Lazar

We introduce a novel extension of reflection calculus, $\mathsf{R}{\mathsf{C}}_{\mathsf{BI}}$, to analyze a family of extensions of ${\mathsf{ACA}}_0$ generated by uniform $\omega$-model and syntactic reflec…